While compliant grippers have become increasingly commonplace in robot manipulation, finding the right stiffness and geometry for grasping the widest variety of objects remains a key challenge. Adjusting both stiffness and gripper geometry on the fly may provide the versatility needed to manipulate the large range of objects found in domestic environments. We present a system for actively controlling the geometry (inflation level) and compliance of Soft-bubble grippers -air filled, highly compliant parallel gripper fingers incorporating visuotactile sensing. The proposed system enables large, controlled changes in gripper finger geometry and grasp stiffness, as well as simple in-hand manipulation. We also demonstrate, despite these changes, the continued viability of advanced perception capabilities such as dense geometry and shear force measurement -we present a straightforward extension of our previously presented approach for measuring shear induced displacements using the internal imaging sensor and taking into account pressure and geometry changes. We quantify the controlled variation of grasp-free geometry, grasp stiffness and contact patch geometry resulting from pressure regulation and we demonstrate new capabilities for the gripper in the home by grasping in constrained spaces, manipulating tools requiring lower and higher stiffness grasps, as well as contact patch modulation.